Question

Complete parts ​(a) through ​(c) below.

a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the α = 0.10 level of significance with 15 degrees of freedom.
​b) Determine the critical​ value(s) for a​ left-tailed test of a population mean at the α = 0.10 level of significance based on a sample size of n = 20.
c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the α = 0.05 level of significance based on a sample size of n = 18.

Answer 1

a)
`t_(crit)=1.34`

b)
`t_(crit)=-1.33`

c)
`t_(crit)=\pm 2.11`

Explanation:

Part a

`\alpha=0.1` represent the significance level

df =15

Since is a right tailed test the critical value is given by:

`t_(crit)=1.34`

And we can use the following excel code to find it: "=T.INV(0.9,15)"

Part b

`\alpha=0.1` represent the significance level

n=20 represent the sample size

First we need to find the degrees of freedom given by:

`df=n-1=20-1=19`

Since is a left tailed test the critical value is given by:

`t_(crit)=-1.33`

And we can use the following excel code to find it: "=T.INV(0.1,19)"

Part c

`\alpha=0.05` represent the significance level

n=18 represent the sample size

First we need to find the degrees of freedom given by:

`df=n-1=18-1=17`

The value of
`\alpha=0.05` and
`\alpha/2 =0.025`

Since is a two tailed tailed we have two critical values is given by:

`t_(crit)=\pm 2.11`

And we can use the following excel code to find it: "=T.INV(0.025,17)"